The class of shift-equivariant kernels has a desirable property that they can be decomposed as a linear combination of eigen functions.
Eigen transforms have a magical property where according to the convolution theorem [1]}, global convolution in the spatial domain amounts to multiplication in the eigen transform domain. A popular example of such eigen functions is the Fourier transform. Accordingly, one can define the Fourier neural operator (FNO) [2]}.
